Moussa has undertaken two days of talks with political leaders, but has been unable to break the deadlock and said the "sharpness of the tension" had to be fixed.
Politicians have agreed on a compromise candidate, General Michel Suleiman, the army chief.
Moussa said his selection was valid. However, the parliament must amend the constitution to allow a sitting military chief to be elected.
Moussa, on his second visit to the Lebanese capital this year, hosted the talks with Saad al-Hariri, the majority leader, Michel Aoun, the Christian opposition leader, and Amin Gemayel, a former president who is aligned with the anti-Syrian majority bloc.
The discussion focused on ways of implementing a three-point Arab League plan calling for the election of Suleiman as president, the formation of a national unity government and the adoption of a new election law.
The plan was unanimously adopted by Arab foreign ministers in Cairo, Egypt, last month.
Moussa said the two sides still supported Suleiman and showed "a common desire" to reach a solution to the presidential crisis, but he refused to say what issues were holding up an agreement.
An official close to Berri's entourage said the speaker was trying to convince his camp to agree on a formula in which the Western-backed ruling coalition, the Hezbollah-led opposition and the new president would each have 10 ministers in a new government.
The majority and the opposition had previously rejected this scenario with each insisting on having more leverage.
A parliament session to elect a president has been postponed 13 times. The next session is due on Monday.